Abstract
In this chapter, we introduce Riemann surfaces and prove an important theorem which asserts that meromorphic functions on a compact Riemann surface form an algebraic function field in one variable (see §6). The chapter is meant to serve as an introduction to some tools which have proved to be very useful in several branches of mathematics, in particular, in several complex variables and algebraic geometry.
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Narasimhan, R., Nievergelt, Y. (2001). Compact Riemann Surfaces. In: Complex Analysis in One Variable. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0175-5_9
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DOI: https://doi.org/10.1007/978-1-4612-0175-5_9
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4612-6647-1
Online ISBN: 978-1-4612-0175-5
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